Three-Dimensional Bin Packing in Mixed-case Palletization

The Three Dimensional Bin Packing Problem (3DBPP) is within one of the broad categories of the Bin Packing Problem. The other broad categories include the One Dimensional and the Two Dimensional Bin Packing Problem. As we live in a three dimensional world, the 3DBPP can model a variety of real world problems. Some of the popular applications of the 3DBPP include the Container Loading Problem and the Pallet Packing Problem. The objective of the 3DBPP is to minimize the number of containers or pallets used given a certain number of items, while respecting the non-overlapping constraints along all three dimensions. The Open Dimension Problem (ODP), is a special case of the 3DBPP, where a given set of cargo is packed onto a single container, with one or more variable dimensions. The Single Bin Size Bin Packing Problem (SBSBPP) is another special case, where a given set of cargo is packed in bins of the same size, with the objective of minimizing the number of bins used. The SBSBPP is more difficult to solve than the ODP, as items are packed in multiple bins in the SBSBPP and in only one bin in the ODP. In this thesis, we first propose a mixed-integer programming model for the ODP, where the objective is to minimize the highest point within the bin. We then provide a number of enhancements to improve the model. Later, a number of heuristics are proposed to find good feasible solutions within reasonable computational time. Finally the solution of the ODP is used to provide a solution to the SBSBPP. The proposed approach is compared to well-known approaches from the literature on a standard data set. The approach was able to give reasonably good solutions to most instances within a given time frame, especially when the number of items per bin increases.